I don't necessarily have a 'planted' tank with sand/soil and lots of greenery. I do have a 5 gallon cycled tank with gravel substrate that holds down a java fern and a pennywort plant.

That being said, is there anything I need to be doing for these plants to meet their needs? I have a day-night timer that keeps the light on from about 7:30 in the morning till 10 at night (hopefully that's not too long...) but otherwise, nothing but the waste my one Betta-boy produces to lend nutrients.

I did happen upon some fertilizer tablets at the petstore, does anyone recommend I use them in this situation? Will it change the chemistry of my tank? It's only been cycled for a week, and it was quite a bit of work to get it to this point.

I wouldn't use tablets (for one thing, the java fern can't utilise them). If your plants appear to be struggling with just the betta poop, then a little liquid supplement like Flourish can give it a boost, but if the plants are healthy, don't bother - excess supplements will just cause algae. :)

I hope you don't mean the the java fern is planted into the gravel like a normal plant. Java fern needs the rhizome to be above the substrate or it will rot.

Assuming you're just using the standard hood fixture that comes with the tank, you should't need to supplement anything into the tank. Plants grow slowly under low light and can only use nutrients as quickly as they're growing which is why many people like the concept of low-light planted tanks. As you increase the lighting, you may need to start dosing ferts and possibly injecting CO2. But for your tank, the decomposition within the tank should suffice. What you can do is keep an eye on nutrient deficiency symptoms and that will tell you if anything needs to be added.